Keywords: Menger space; weakly compatible mappings; occasionally weakly compatible mappings; fixed point
@article{AUPO_2013_52_1_a4,
author = {Chauhan, Sunny and Pant, B. D.},
title = {Some {Common} {Fixed} {Point} {Theorems} in {Menger} {Spaces}},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
pages = {57--69},
year = {2013},
volume = {52},
number = {1},
mrnumber = {3202749},
zbl = {1285.54032},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AUPO_2013_52_1_a4/}
}
TY - JOUR AU - Chauhan, Sunny AU - Pant, B. D. TI - Some Common Fixed Point Theorems in Menger Spaces JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica PY - 2013 SP - 57 EP - 69 VL - 52 IS - 1 UR - http://geodesic.mathdoc.fr/item/AUPO_2013_52_1_a4/ LA - en ID - AUPO_2013_52_1_a4 ER -
Chauhan, Sunny; Pant, B. D. Some Common Fixed Point Theorems in Menger Spaces. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 1, pp. 57-69. http://geodesic.mathdoc.fr/item/AUPO_2013_52_1_a4/
[1] Abbas, M., Rhoades, B. E.: Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition. Math. Commun. 13, 2 (2008), 295–301. | MR | Zbl
[2] Ali, J., Imdad, M., Miheţ, D., Tanveer, M.: Common fixed points of strict contractions in Menger spaces. Acta Math. Hungar. 132, 4 (2011), 367–386. | DOI | MR | Zbl
[3] Al-Thagafi, M. A., Shahzad, N.: Generalized $I$-nonexpansive selfmaps and invariant approximations. Acta Math. Sinica (English Series) 24, 5 (2008), 867–876. | DOI | MR | Zbl
[4] Al-Thagafi, M. A., Shahzad, N.: A note on occasionally weakly compatible maps. Int. J. Math. Anal. (Ruse) 3, 2 (2009), 55–58. | MR | Zbl
[5] Bharucha-Reid, A. T.: Fixed point theorems in probabilistic analysis. Bull. Amer. Math. Soc. 82, 5 (1976), 641–657. | DOI | MR | Zbl
[6] Bhatt, A., Chandra, H., Sahu, D. R.: Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions. Nonlinear Analysis 73, 1 (2010), 176–182. | DOI | MR | Zbl
[7] Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math. 3 (1922), 133–181.
[8] Chandra, H., Bhatt, A.: Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space. Int. J. Math. Anal. 3, 12 (2009), 563–570. | MR | Zbl
[9] Chang, S. S., Cho, Y. J., Kang, S. M.: Nonlinear Operator Theory in Probabilistic Metric Spaces. Nova Science Publishers, Inc., New York, 2001. | MR | Zbl
[10] Chauhan, S., Dhiman, N.: Common fixed point theorems on fuzzy metric spaces using implicit relation. Math. Sci. Lett. 1, 2 (2012), 89–96. | DOI
[11] Chauhan, S., Kumar, S.: Fixed points of occasionally weakly compatible mappings in fuzzy metric spaces. Sci. Magna 7, 2 (2011), 22–31.
[12] Chauhan, S., Kumar, S.: Fixed point theorems in Menger spaces and applications to metric spaces. J. Appl. Math. Inform. 30, 5-6 (2012), 729–740. | MR
[13] Chauhan, S., Kumar, S., Pant, B. D.: Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces. J. Adv. Research Pure Math. 3, 4 (2011), 17–23. | DOI | MR
[14] Chauhan, S., Pant, B. D.: Common fixed point theorems for occasionally weakly compatible mappings using implicit relation. J. Indian Math. Soc. (N.S.) 77, 1-4 (2010), 13–21. | MR | Zbl
[15] Chauhan, S., Pant, B. D.: Common fixed point theorems in fuzzy metric spaces. Bull. Allahabad Math. Soc. 27, 1 (2012), 27–43. | MR | Zbl
[16] Chauhan, S., Pant, B. D., Dhiman, N.: A common fixed point theorem in Menger space. Sci. Magna 8, 1 (2012), 73–78. | MR
[17] Ćirić, Lj. B.: On fixed points of generalized contractions on probabilistic metric spaces. Publ. Inst. Math. (Beograd) (N.S.) 18, 32 (1975), 71–78. | MR | Zbl
[18] Ćirić, Lj. B., Razani, A., Radenović, S., Ume, J. S: Common fixed point theorems for families of weakly compatible maps. Comput. Math. Appl. 55, 11 (2008), 2533–2543. | DOI | MR | Zbl
[19] Ćirić, Lj. B., Samet, B., Vetro, C.: Common fixed point theorems for families of occasionally weakly compatible mappings. Math. Comp. Model. 53, 5-6 (2011), 631–636. | MR | Zbl
[20] Fang, J.-x.: Common fixed point theorems of compatible and weakly compatible maps in Menger spaces. Nonlinear Anal. 71, 5-6 (2009), 1833–1843. | MR | Zbl
[21] Fang,J.-x., Gao, Y.: Common fixed point theorems under strict contractive conditions in Menger spaces. Nonlinear Anal. 70, 1 (2009), 184–193. | DOI | MR | Zbl
[22] Hicks, T. L.: Fixed point theory in probabilistic metric spaces. Zbornik Radova, Prir.-Mat. Fak., Univerzitet u Novom Sadu 13 (1983), 63–72. | MR | Zbl
[23] Hicks, T. L., Sharma, P. L.: Probabilistic metric structures: Topological classification. Zbornik Radova, Prir.-Mat. Fak., Univerzitet u Novom Sadu 14, 1 (1984), 35–42. | MR | Zbl
[24] Imdad, M., Ali, J., Tanveer, M.: Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces. Chaos, Solitons & Fractals 42, 5 (2009), 3121–3129. | DOI | MR | Zbl
[25] Jungck, G.: Common fixed points for commuting and compatible maps on compacta. Proc. Amer. Math. Soc. 103, 3 (1988), 977–983. | DOI | MR | Zbl
[26] Jungck, G.: Common fixed points for noncontinuous nonself maps on nonmetric spaces. Far East J. Math. Sci. 4, 2 (1996), 199–215. | MR | Zbl
[27] Jungck, G., Rhoades, B. E.: Fixed point theorems for occasionally weakly compatible mappings. Fixed Point Theory 7, 2 (2006), 286–296. | MR | Zbl
[28] Kasahara, S., Rhoades, B. E.: Common fixed point theorems in compact metric spaces. Math. Japonica 23, 2 (1978/79), 227–229. | MR | Zbl
[29] Liu, Y., Wu, J., Li, Z.: Common fixed points of single-valued and multi-valued maps. Int. J. Math. Math. Sci. 19 (2005), 3045–3055. | DOI | MR
[30] Menger, K.: Statistical metrics. Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 535–537. | DOI | MR | Zbl
[31] Menger, K.: Probabilistic geometry. Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 226–229. | DOI | MR | Zbl
[32] Pant, R. P.: Common fixed points of noncommuting mappings. J. Math. Anal. Appl. 188, 2 (1994), 436–440. | DOI | MR | Zbl
[33] Pant, R. P.: Common fixed point theorems for contractive maps. J. Math. Anal. Appl. 226, 1 (1998), 251–258. | DOI | MR | Zbl
[34] Pant, R. P.: $R$-weak commutativity and common fixed points. Soochow J. Math. 25, 1 (1999), 37–42. | MR | Zbl
[35] Pant, R. P., Pant, V.: Common fixed points under strict contractive conditions. J. Math. Anal. Appl. 248, 1 (2000), 327–332. | DOI | MR | Zbl
[36] Pant, B. D., Chauhan, S.: Common fixed point theorem for occasionally weakly compatible mappings in Menger space. Surv. Math. Appl. 6 (2011), 1–7. | MR
[37] Pant, B. D., Chauhan, S.: Common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces and application. Bull. Allahabad Math. Soc. 26, 2 (2011), 285–306. | MR | Zbl
[38] Pant, B. D., Chauhan, S.: Common fixed point theorems for occasionally weakly compatible mappings in Menger probabilistic quasi-metric spaces. Adv. Nonlinear Var. Ineq. 14, 2 (2011), 55–63. | MR | Zbl
[39] Pant, B. D., Chauhan, S.: Fixed points of occasionally weakly compatible mappings using implicit relation. Commun. Korean Math. Soc. 27, 3 (2012), 513–522. | DOI | MR | Zbl
[40] Pant, B. D., Chauhan, S.: Fixed point theorems for occasionally weakly compatible mappings in Menger spaces. Mat. Vesnik 64, 4 (2012), 267–274. | MR | Zbl
[41] Pant, B. D., Chauhan, S., Fisher, B.: Fixed point theorems for families of occasionally weakly compatible mappings. J. Indian Math. Soc. (N.S.) 79, 1-4 (2012), 127–138. | MR
[42] Pant, B. D., Kumar, S., Chauhan, S.: Fixed points of occasionally weakly compatible mappings in Menger spaces. Bull. Calcutta Math. Soc. 104, 1 (2012), 11–20. | MR
[43] Pant, B. D., Samet, B., Chauhan, S.: Coincidence and common fixed point theorems for single-valued and set-valued mappings. Commun. Korean Math. Soc. 27, 4 (2012), 733–743. | DOI | MR
[44] Razani, A., Shirdaryazdi, M.: A common fixed point theorem of compatible maps in Menger space. Chaos, Solitons & Fractals 32, 1 (2007), 26–34. | DOI | MR | Zbl
[45] Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific J. Math. 10 (1960), 313–334. | DOI | MR | Zbl
[46] Schweizer, B., Sklar, A.: Probabilistic metric spaces. North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing Co., New York, 1983. | MR | Zbl
[47] Sehgal, V. M.: Some fixed point theorems in functional analysis and probability. Wayne State Univ., Detroit, 1966, Ph. D. Dissertation. | MR
[48] Sehgal, V. M., Bharucha-Reid, A. T.: Fixed points of contraction mappings on probabilistic metric spaces. Math. Systems Theory 6 (1972), 97–102. | DOI | MR | Zbl
[49] Singh, B., Jain, S.: A fixed point theorem in Menger space through weak compatibility. J. Math. Anal. Appl. 301, 2 (2005), 439–448. | DOI | MR | Zbl
[50] Vetro, C.: Some fixed point theorems for occasionally weakly compatible mappings in probabilistic semi-metric spaces. Int. J. Modern Math. 4, 3 (2009), 277–284. | MR | Zbl